Pentagram combinations in a decagonal frame
Sándor Kabai
Pentagrams are created within a decagonal frame. Compare the hexagonal version: https://community.wolfram.com/groups/-/m/t/2993419
Pentagrams are created within a decagonal frame. Compare the hexagonal version: https://community.wolfram.com/groups/-/m/t/2993419
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fi=GoldenRatio;c10=Tube[Table[{Sin[i2Pi/10],Cos[i2Pi/10],0},{i,10+1}],0.018];y=Sin[2Pi/20];x=Cos[2Pi/20];k=Sin[2Pi/10];h=Cos[2Pi/10];vM={0,1,0};vMB={x/fi^3,y,0};vB={x,y,0};angle=Tube[{vM,vMB,vB},0.01];angle10=Table[Rotate[{angle},i2Pi/10,{0,0,1}],{i,10}];vE={k,h,0};vF={-k,h,0};e1=Tube[{vE,vF},0.01];e10=Table[Rotate[{e1},i2Pi/10,{0,0,1}],{i,10}];vE1={k+0.2,h-0.3,0};vF1={-k-0.2,h-0.3,0};f1=Tube[{vE1,vF1},0.01];f10=Table[Rotate[{f1},i2Pi/10,{0,0,1}],{i,10}];frame=Table[{Sin[i2Pi/5],Cos[i2Pi/5],0},{i,0,8,2}];p1={Polygon[frame]};p2=Scale[p1,1/fi^2{1,1,1},{0,0,0}];p3=Table[Rotate[Translate[Scale[p1,1/(fi^2+1){1,1,1},{0,0,0}],{0,0.72,0}],i2Pi/5+Pi/5,{0,0,1}],{i,5}];Graphics3D[{Yellow,p3,Cyan,p1,Yellow,p2,Cyan,f10,Pink,e10,Green,angle10,Yellow,c10},ImageSize400,Boxed->False,ViewPoint->{0,0,100},SphericalRegion->True]
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Graphics3D[{Cyan,f10,Pink,e10,Green,angle10,Yellow,c10},ImageSize400,Boxed->False,ViewPoint->{0,0,100},SphericalRegion->True]
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p21=Scale[Rotate[p1,Pi,{0,0,1}],1/fi^2{1,1,1},{0,0,0}];p11=Rotate[p1,Pi,{0,0,1}];Graphics3D[{p11,Yellow,p3,Cyan,p1,Yellow,p21,Cyan,f10,Pink,e10,p2,Green,angle10,Yellow,c10},ImageSize400,Boxed->False,ViewPoint->{0,0,100},SphericalRegion->True]
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(*RelatedtothePentartsystem:https://demonstrations.wolfram.com/PentagonalArtTemplate/*)ϕ=GoldenRatio;u=24;w1={Thickness[0.0005],Line[{{{0,-u,0},{0,u,0}},{{ϕ,-u,0},{ϕ,u,0}},{{ϕ+1,-u,0},{ϕ+1,u,0}},{{2ϕ+1,-u,0},{2ϕ+1,u,0}},{{2ϕ+2,-u,0},{2ϕ+2,u,0}},{{3ϕ+2,-u,0},{3ϕ+2,u,0}},{{4ϕ+2,-u,0},{4ϕ+2,u,0}},{{4ϕ+3,-u,0},{4ϕ+3,u,0}},{{5ϕ+3,-u,0},{5ϕ+3,u,0}}}]};w2=Translate[w1,{5ϕ+3,0,0}];w={w1,w2};w5=Table[Rotate[w,i2Pi/10,{0,0,1}],{i,10}];x=5ϕ+3;y=xTan[2Pi/20];vA={x,y,0};d=Sqrt[x^2+y^2];vB={x,y+d,0};vC={0,d,0};vD={0,0,0};vE={0,d+2y,0};vF={-x,y+d,0};p1={Thickness[0.005],Line[{vD,vA,vB,vC}]};star=Table[Rotate[p1,i2Pi/5,{0,0,1}],{i,5}];pe1={Thickness[0.005],Line[{vB,vE,vF}]};dec=Table[Rotate[pe1,i2Pi/5,{0,0,1}],{i,5}];c10a=Rotate[Scale[{p2,Yellow,p3,Green,f10,Red,e10,Yellow,c10,Cyan,angle10,p11},22{1,1,1},{0,0,0}],Pi/10,{0,0,1}];Graphics3D[{w5,c10a},ImageSize500,ImageSizeTiny,BoxedFalse,SphericalRegionTrue,ViewPoint{0,0,100}]
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